h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Yeah, this is quite interesting. I've now read everything. Were talking from different perspectives and to a small extent talking past each other. Virus is looking at things from the perspective of us developing concepts, elaborating on them, and then looking at things from the framework we have constructed and developing further concepts from that. So, to a large extent, the totality of our knowledge is something that we construct from a few

Yeah, this is quite interesting. I've now read everything. Were talking from different perspectives and to a small extent talking past each other. Virus is looking at things from the perspective of us developing concepts, elaborating on them, and then looking at things from the framework we have constructed and developing further concepts from that. So, to a large extent, the totality of our knowledge is something that we construct from a few first assumptions - axioma. This is more or less the same thing that JD describes as starting from "I think, therefore I am" and ending up with rice pudding and income tax.

I agree, we construct a framework of knowledge, and we develop new concepts based on existing concepts. But somewhere along the line things are thrown in from outside. For instance, the Uncertainty principle is based on reasoning, but not JUST reasoning. They constructed it because they did experiments and observed something they did not expect to observe. So they formulated a theory to render this observation explicable and also to provide a framework for predicting and understanding future observations. But still there are quantities that are measured by observation. Given the framework of the Uncertainty Principle, the value of Planck's constant can be measured by experiment - but still it is a factor that seems to be independent of theories alone, it comes in from the outside through observation.

The thing with the quest for the Theory of Everything, which I have referred to many times now, is that scientists want to come up with a theory that shows all other theories to be logical outcomes of a few small truths - whether axiomatic, or not. So the goal of such a theory would be that you have, at the bottom of the pyramid of human knowledge, a small set of laws/equations and these laws themselves must seem to be perfectly obvious, logical, consistent, it must seem as if it couldn't be any other way. This theory must explain not only why the laws look like they do, it must explain why you get the specific particles and forces that you observe, and it must explain why all physical constants have the values they are observed to have. So the theory must explain why the universe is made of matter and not anti-matter, it must explain why the speed of light is 300 million meters a second and not some other value, and so on and so on. It must explain why the big bang happened and why it went the way it did. It must make all these explanations as logical, inevitable outcomes of the underlying laws, and in a way that does not depend on observations. We have measured the speed of light to be what it is, but the theory of everything must necessarily predict the speed of light to be that value, and no other, independent of our measurements.

In a way such a theory will make observations obsolete. All observations would be predictable by elaborating the theory to a sufficient extent. But in practice this will be too complicated so we will still do lots of experiments.

The belief that such a theory might be found is based on some core assumptions. The theory itself, or any attempt at such a theory, will therefore carry these assumptions into its framework. The question is, how can we believe that such a step would be justified - how can we believe that the universe really does conform to our expectations all the way to the bottom?

The whole issue of the theory of everything is just the enterprise of science carried to an extreme. It should make us think about just what science, and scientific knowledge, really is. Can you see that this extreme more or less connects up our different approaches?

This is all great stuff. We may not all agree but we do seem to understand what we are each talking about which, given the topic, is remarkable.

I suppose that saying all is tautology does sound nihilistic but it is not in fact. I suspect I am not as careful with my word meanings as JD, something I'll have to watch. By tautology I mean just that the truth or otherwise of the statement is intrinsic to the statement, true or false simply be dint of our definition of the words used.

However this is not the end of Guinness and Bach, God forbid. It is based on an explanation of things that allows all other explanations of things to be to some degree true. It is the set of all sets idea, the fact that any true and complete explanation must explain the apparent truth of all other explanations. The Guiness is both real and conceptual, not half one or half the other, but both. Guinness and the Bach Toccata make intersting examples because quite clearly both 'real' things started out as concepts, we made them real, brought them into existence. (Red herring really - this is a weak example of reality as concept)

The point about which concept you start the explanation with is also interesting. Straight logic says that if you start with any belief, any observation, of the Universe the full explanation of it leads to an explanation of the whole Universe (try it). So it does not matter where you start you MUST end up in the same place if the explanation is complete.

By the way if you come across anything about fuzzy logic and neural nets it sheds intersting light on how concepts arise from randomness.

A fundamental truth is, I believe, that randomness is impossible. Structure MUST arise. This much is now virtually accepted as proven. Following, by a devious train of logic, from this is the conclusion that the Universe MUST exist. And all possible things MUST exist. Can't explain this now but I think I can given time later.

On the scientific method I just want to make clear that I am not suggesting it does not work. It works brilliantly in the job it set out to do. And we must continue to apply it and explore it with complete rigour. All I am saying is that ultimately it won't end this converation, it can not get at the fundamental truths. All it can do is describe the observed consequences of those fundamental truths.

UMP is right about my view of concepts, but suggests that something else is thrown in from outside which is non-conceptual. That may be the case, but how the hell do you decide which is which?

Wish I could go on but must dash.

Afterthought - when I refer to things being conceptual I do not necessarily mean conceived by human conciousness, just by a conciousness. Clearly we could not be here unless there was something before us. More on this later too.

I'm enjoying this now. UMP said this: "The whole issue of the theory of everything is just the enterprise of science carried to an
extreme. It should make us think about just what science, and scientific knowledge, really is. Can you see that this extreme more or less connects up our different approaches?" Ah! I think I'm starting to see your point. Yes, I have to agree that the whole point of a GUT is really science carried out to it's logical extreme, or end, for lack of a better term. I like the idea of our different approaches arriving at a single end, or at least having the same goal. I couldn't agree more with that, in fact.

Guys, forgive my sensitivity about the scientific method, by the way. I've been annoyed by its misuse and abuse enough that I tend to overreact a bit when touting its relative advantages. I quite readily accept that it is not the end-all be-all of thought or philosophies - I just wish that more philosophers study physics and mathematics a bit more and vice versa. Oh, and the reason I'm very careful about word usage is 'cos it's a habit I learned quickly being a nuclear safety engineer that works for the Federal Government.

Virus I chipped in with this: "Afterthought - when I refer to things being conceptual I do not necessarily mean conceived by human conciousness, just by a conciousness. Clearly we could not be here unless there was something before us." Ah, but then what came before THAT entity? Ever read Hawking's "A Brief History of Time"? I recommend it. Very fascinating and has a lot to do with what we're talking about. I'd be surprised if UMP hasn't read it, as a lot of what he is saying is very similar to Hawking's writings, though Hawking himself updated the book in '98 to reflect some of the major changes in ideas he's had over the ten years since he wrote it in '88.

Some other interesting points from UMB: "In a way such a theory will make observations obsolete. All observations would be
predictable by elaborating the theory to a sufficient extent. But in practice this will be too complicated so we will still do lots of experiments." I think this is something of a primer for Gödel's theory of incompleteness, which in essence states that we can't know everything. It's quite fascinating in it's implications. It ultimately means that a theory that predicts everything cannot exist. I'm not extremely familiar with the exact mathematical details of his theory, but it seems to agree with my own personal logic, which is decidedly un-mathematical in this respect. The way I see it, a theory cannot predict everything that can happen (or thus make observation obsolete); it cannot really exist because, quite simply, it cannot ever be tested, and that is the heart of theory. Yes, there are several theories that start off as empirical mathematical expressions expressing only what we have observed already - in effect, a translation of the observations into the language of science - but no predictions are made for the phenomena that have not been observed, or no explanation has been provided for WHY the expression holds true. For example, at first it seemed Planck's equation that solved the problem of accurately predicting the spectral emittance of a blackbody seemed to merely fit the experimentally observed data, and existed for a some years without a theoretical explanation. His empiracal explanation of how light and energy are quantized (i.e. they come in sort of "packets" of energy, more like waves that particles) was ultimately given a theoretical basis by Werner Heisenberg with his uncertainty relations, and his help in founding the theory of quantum mechanics. Equations and relations that are based purely on observations are really not theories - they are simply mathematical expressions for a phenomenon - translations, if you will, of the real world into the language of science. A total, grand unified theory of everything (although I'm using this term slightly improperly here) should explain, as you pointed out, all phenomena that can be observed ... ideally, in effect, eliminating the need for observation at all. Perhaps it is a small comfort then, that as Gödel apparently has proven, we cannot know everything, thus leaving room for the fact that we will always need to observe.

UMB also said: "The belief that such a theory might be found is based on some core assumptions. The theory itself, or any attempt at such a theory, will therefore carry these assumptions into its framework. The question is, how can we believe that such a step would be justified - how can we believe that the universe really does conform to our expectations all the way to the bottom?" Well, that all depends on the assumption being made. Did you have anything specific in mind? Or are you merely pointing out the inherent flaw of science being based on some ultimate assumption? Quite a number of fundamental assumptions in science have been overturned in the last 50 years or so, starting with the most basic assumptions made in classical physics. Everyone, from Galileo Galilei to Newton to Einstein to Schrödinger to Heisenberg to Hawking has had erroneous assumptions proven wrong at one time or another. Major ones, too, not just the "I'm sorry Honey, I assumed you heard me when I said I was going to stop off for a few pints with the lads" variety. In fact, with Gödel's relatively new theory of incompleteness making its impact even now, it seems that we're living in time of major upheaval and change as far as classical physical concepts and assumptions are concerned. I still maintain a faith in the whole way of thought inherent in scientific method - it can, and does, repair itself and evolve as it goes along. Perhaps it will repair itself so extensively that it it can hardly be called by the same name; that is, perhaps a new method of thought will come out of our efforts to think about the fundamental nature of the Universe, a method that allows for us to think about it in its own terms instead of our own terms, in effect becoming more an integral part of the Universe as we understand it more. Maybe becoming a more integral part of the Universe and explaining it more are so intertwined as to be causes and effects of each other - a sort of self-reinforced feedback loop that will continue to accelerate human thought to the level and kind necessary to BE the Universe itself ...

Either that, or think ourselves out of safety and into the true danger of too much power. Who can tell?

- JD

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Yes, I've read "A Brief History of Time". I don't agree with everything but I find it a very good example of an eminent scientist talking about the enterprise of science. We have to listen to what they say to understand what they believe themselves to be doing. What's interesting to me is that different scientists will have wildly diverging ideas about what they're doing, and this suggests to me that science is not really the solid monolith that it is made out to be. This does not mean that it is without value, only that we need to look at it a bit more closely and critically so we can discern the cracks in it and not put our trust in it too blindly. But there are enough solid bits that they can provide some kind of foundation for building an understanding of the universe.

Virus, Gödel's Incompleteness Theorem does not say anything about theories explaining things. It says something about logical frameworks, or "formal systems". What Gödel found out is this: no logical framework, or formal system, can be completely self-consistent! There will always be little pieces that doesn't fit. He formulated it by proving that in Number Theory there are statements that are true but cannot be proven to be true using the axioma of that theory combined with logic. And here "proof" is a rigorous definition: a proof is merely a statement of Number Theory itself, formulated as a combination of axioma and logic symbols. This is a real and undeniable paradox, because the axioma of Number Theory are things that are supposed to be always true, and the rules of logic are supposed to give absolute certainty about the truth or falseness of statements when applied to axioma.

Gödel extended this discovery into saying that every system that is based on certain axioma, and logic, will be incomplete. If you take those axioma, whatever they may be, and elaborate on them by using the rules of logic, sooner or later you will be faced with a contradiction. Number theory is the most rigorous formal system that exists - a more rigorous system cannot be imagined - and if IT is not fully self-consistent, then nothing is.

I want to point out something: in mathematics, axioma can be chosen with complete freedom. When you choose one set of axioma, you get one kind of mathematics; when you choose a different set of axioma, you get a different kind of mathematics. The axioma don't have to correspond to anything in reality - they merely provide conceptual bases for different formal systems. In science, however, you have to find/choose axioma that correspond to the Truth about Reality. Some axioma of Science are that Reality exists, makes sense, and can be figured out. To put it differently, we can conceive a formal model of the Universe that describes it completely for our purposes, but that is smaller than the totality of the Universe. The whole can be reduced to a model smaller than itself. There are probably other axioma as well, but these are the most essential ones. Applying Gödel's Incompleteness Theorem, we now find that if we take these axioma and try to deduce further truths about the Universe from them, we will sooner or later run into an inconsistency: at least one statement that cannot be decided from within the system. We have to jump out of the system and decide on the truth of the statement from the outside. We have to abandon some of the axioma, or some of the rules of logic applied to them. So the system is not complete in itself.

A possibility exists that we may need a number of different formal systems for describing the universe. In other words, formal science, but also at least one other system. Then the gap left by one can be filled by the other.

UMP - I wasn't suggesting Godel said anything about theories, in fact I was trying to say that he wasn't. However, are you sure about what you said? I thought Godel said you could not prove any logical system to be free of contradictions, not that no wholly consistent system could exist. I would like to know which of these is correct because it's a big difference. I suspect that he did not say that "sooner or later you will be faced with a contradiction" but rather that you can not be certain that you will not be faced with a contradiction.

I like your idea that 'incompleteness' means that we may need a number of different systems to explain/describe things properly. However I suspect logic shows that in the end they wouldn't be able finish the job for the same reason they couldn't finish it individually.

I am a bit confused about what Godel proved about incompleteness as opposed to consistency/contradiction. Are these the same point are are they two different things? Incompleteness, as you describe it, is something I can grasp, in fact with my simplistic understanding it seems close to common sense, but a complete uncertainty as to the internal coherence of a system is something different. Does one follow from the other, are they different points, or did he only prove one of them?

The axiom thing is the root of so many problems. How can we ever know that our axioma (is 'axioms' OK common usage? I prefer it.) are correct. By definition it seems that we can not. However I think we can approach the search for an explanation by asking how it is that we come to believe that certain axioma are correct. We may not know what is there but we know for certain what we believe - and any explanation must explain the cause of these beliefs. If we can explain the cause of our beliefs then we've done it - that would be good enough. It wouldn't matter what was really there, we would have explained whatever was really there by the back door. This is a roundabout route back to my point about concepts. It is our concepts we have to explain, not 'reality', as if reality was something different. I am fairly certain it can be shown that we can never ever know whether our concept of reality and reality itself are different or one and the same. We are stuck with trying to explain what we believe.

Taking this further than it should probably go - A theory that could explain all possible beliefs would explain the Universe. Or, to put it a little better, an explanation of the Universe that would encompass all possible beliefs about it is going to be about the best we can ever do. And it would be a real GUT, not something restricted to a few post Big Bang material bits with no origin.

Just a fast one today: I'll try to clarify Gödel a bit more. I suspected that I would have to. The best way to understand the theorem is to go into the detail of the mathematics - there oughta be something about it on the internet, maybe right here on h2g2.

In Gödel's Incompleteness Theorem, inconsistency means that a paradox occurs. You have axioma, and you have the rules of logic, and you go on deducing new theorems from them with mathematical rigour. Everything is supposed to follow straightforwardly. But then at a point you get a paradox. You backtrack, but you discover that you haven't made any mistakes.

I used the word "paradox", which is not exactly the same as a contradiction. A paradox is any kind of logical dilemma, not just a contradiction. A contradiction is when you statements that negate each other, for instance "It is raining" and "It is not raining". According to strict logic both cannot be true at the same time. A paradox is a little different from a contradiction - a paradox would occur when a contradiction actually is true, for example. But another example of a paradox would be an undecidable statement in formal logic. Formal logic has absolutely strict rules, and by those rules, if you have a group of statements considered to be true, you should ALWAYS be able to decide the truth or falsity of statements derived from the initial statements by using the rules. So when you start with statements considered true, and operate on them using logical rules, you should always end up with statements that can be clearly shown to be either true or false. So if you get a statement that cannot be shown to be either true or false, that is a paradox. Gödel's theorem involves this kind of paradox, but it can probably also be framed as a contradictory statement. I'm not exactly certain - I'll go look up the details a bit if I have time.

Gödel did not say that you cannot be certain that you will not be faced with a paradox. He produced a paradox so that everybody could see it. That's the method of "disproof by example". Suppose I say, "all crows are black". This can be disproved by a single example of a crow that is not black (I suggest the Grey Crow, Corvus tristis, of New Guinea). A single example is enough. If there is one crow that is not black, then the statement "all crows are black" is false. There might be many other kinds of crows that aren't black (as indeed there are). But you only need one for the purposes of disproof. In the same way Gödel took one formal system, which is based on axioma and rules of deduction based on formal logic, and demonstrated that a paradox can be produced by following the rules perfectly.

The formal system that Gödel used was Number Theory. This is what Mathematics is based on. It is supposed to be completely logical, and formerly was believed to be free from any inconsistencies/ paradoxes. It was supposed that working within the system you could rigorously prove the truth or falsity of everything that you could say by using its formalisms. Gödel showed that there was at least one thing that couldn't be proved from within the system. Nevertheless, this thing could easily be proven by jumping out of the system. Therefore the system is not complete in and of itself; there has to be an "outside" perspective from which at least some statements needed to be judged. Because Mathematics is the most rigorous discipline that we can imagine, it is a fair conclusion that if IT is not complete in and of itself (that is what self-consistency means) then NOTHING is. So there can be no conceivable system that does not need a perspective outside itself from which some of its own assertions would need to be judged.

So Gödel's Incompleteness Theorem doesn't say anything about theories themselves, but its conclusion is relevant to the conceptual frameworks in which theories are framed. A reasonable conclusion would be that we cannot create a conceptual framework that will be fully self-consistent, in other words that would demonstrate/explain the truth/meaningfullness all the true and meaningful theories that can be expressed in its own jargon. At least some of those theories WILL need to be judged from an "outside" perspective.

Human language is also a formal system, less rigorous than Number Theory. Even while we try to speak as truthfully and as rigorously as we can, we are still producing loads and loads of contradictory statements. An in depth analysis of this forum might be an interesting demonstration!

Any further things needing to be cleared up? I think if we all understand this first, we'll be in a better position to go forward into more nebulous territories.

I think I've got that.

And I think this is strongly related to the reasons that I have suggested that maybe the only meaningful statements about the Universe made in the language of science are incapable of testing or are tautologies.

However I need time to ponder this.

I'll start by pondering out loud. (Isn't 'pondering' an odd word when you repeat it).

If we ever find a true explanation of the Universe, a GUT in the fullest sense of the term, then it will have to be provably undisprovable. As you say, the nature of any scientific proof is that it is disproved by one single contradictory example. As we seem unlikely to ever be able to observe the whole cosmos then any full explanation must be in principle undisprovable. That does not, however, mean that it has to be provable. Any deep and true statement about the Universe is therefore likely to have this characteristic - that it may not be provable and is certainly not disprovable. It then ceases to be what would be considered a meaningful statement by science. This is odd, and rather suggests that science, as we now define it, is in the end inadequate to its task.

I do think this is the case. On the other hand I think the logic I've used here to suggest it is rather weak. I'm still working out how to put this, and the ideas that follow from it, clearly.

I tried to post this yesterday when I wrote it, but H2G2 wouldn't let me, for some bizarre reason. Here it is now:

Virus said: "[The idea that everything has consciousness and there are as many Universes as conciousnesses] is, I suspect, one of those fundamental ideas that might, in different circumstances, have informed our own view of the Universe and thus the evolution of our sciences and philosophies, but which is in principle untestable. It is the kind of question that suggests a real weakness in our insistence on testability by observation." My dear Virus, the only reason it is untestable is because there is no method for testing. You seem to think that there will NEVER be a method for testing that! I personally take a bit more optimistic (and, I think, logical) tack when I say that just because methods for observing or testing consciousness in other beings is not available today that it will never be available in the future - at which point, very good ideas like the one you stated above can be tested. That's an inherent assumption of the scientific method, and one part of which I think a lot of people forget. That is, just because something isn't a "good theory" per strict adherence to the scientific method today, that doesn't mean it will remain a "bad theory" forever, or even that it really is a "bad theory" today. The term "bad theory" should, IMHO, be applied to theories that CAN but are NOT tested by existing means. Quite unlike the field of metaphysics, which is, I think, not under the realm of "bad theory."

Virus also says: "As you say, the nature of any scientific proof is that it is disproved by one single contradictory example. As we seem unlikely to ever be able to observe the whole cosmos then any full explanation must be in principle undisprovable." That logic has always appealed to my way of thinking. But that's where pragmatism comes handy, as I simply shrug my shoulders and say to myself, "well hell, if nothing can be proved right or wrong via direct observation, since I cannot be all conceivable places at all conceivable times, then I might as well do what I can and leave most such things open-ended and recognize the consequences for leaving them open-ended." Which is what I do. But this bit you go on to bothers me: "That does not, however, mean that it has to be provable. Any deep and true statement about the Universe is therefore likely to have this characteristic - that it may not be provable and is certainly not disprovable. It then ceases to be what would be considered a meaningful statement by science. This is odd, and rather suggests that science, as we now define it, is in the end inadequate to its task." I think you have an erroneous idea about what constitutes a meaningful statement of science. I think this misunderstanding is quite widespread, and is contrary to the science practiced by most of the scientists *I* know and work with and was taught by. That is to say, a theory does not have to be "provable" for it to be "testable." You see, testing does NOT constitute proof, since by the very nature of the extent of the Universe versus our own meager and limited extent, we cannot proove or disproove anything. Therefore, we must accept that our theories are, at best, testable and explain the bits of our Universe that we CAN test and observe. This cannot and does not say anything about otehr bits of the universe that we cannot observe or test at the moment; merely that we hope, in many cases of hypothesis and developing theories, that the means for testing and observing will come about in the future. Good theories are, again, those that can be tested; perhaps this definition should include the (admittedly optimistic) assumption that in the future, as techology advances, some theories will eventually become testable and shouldn't be discounted at present. I feel that such a thing is within the existing nature of the scientific method, but I'm also aware that there are several so-called scientists and believers of the scientific method that do not agree with my interpretation - which is what prompted me to write my post to that forum that brought you both here (IIRC); I think that the true heart of science is keeping an open mind and not writing off certain ideas and concepts simply because they are not testable with our present observational abilities - by the same token, such theories are not really "good" theories are present, but they aren't "bad" ones either. Perhaps, though, there are some things that will NEVER be observable. What to do about such ideas?

It is the hope and goal of science to keep trudging on and on through the Universe, explaining it bit by bit as we come across it. What shocked and revolutionized everything was the apparent overturning of the core belief that eventually, given enough time, we as logical-thinking entities would be able to form a complete logical explanation or theory of everything. This was what Gödel demonstrated with his incompleteness theorem; or so I say. That's what I meant by referring to him, and why I made the statement that Gödel's work seemed to indicate that a theory that explains everything cannot exsist. To explain my point, Gödel showed that any logical system cannot be complete AND logically consistent. (again, I rely on what I have read as I am not a mathemetician and only have formally been taught mathematics in the practical areas of Calculus, Ordinary Differential Equations, and Statistics for Engineers) The way I understand it, by making the infamous statement, "this statement is not provable in system S," and applying it to something as basic as Number Theory, he said by implication that all theories are either incomplete or inconsistent since everything is ultimately based on the logic and axioms of Number Theory. I think this is what UMP backed up with his explanation. The infamous statement could also be written as, "this statement is false." THAT is a paradox - something that is both true and false. I merely followed through with the implications and consequences of Gödel's earth-shaking statements to how it affects the logic used in the mathematical formulations relied upon to fully describe ALL theories, including those of general relativity and quantum mechanics. By the way, here's a link to a brief description of Gödel's incompleteness theorem on H2G2: http://www.h2g2.com/A422010 , though I have to agree with a comment made in that forum that the particular paradox used (the so-called Librarian's Paradox) doesn't fully illustrate Gödel's incompleteness theorem, either in explaining it or demonstrating it's effects on science and logic. I'm interested to see if you two (UMP and Virus) agree or not.

Anyhoo, I hope I clarified why I brought up Gödel's incompleteness theorem and why I feel such a theorem affects all logic and thus all scientific theories. UMP put it so succinctly when he said: "A possibility exists that we may need a number of different normal systems for describing the universe. In other words, formal science, but also at least one other system. Then the gap left by one can be filled by the other." I quite agree with this, and have been trying to say this all along! Thanks for putting it so well! I've been saying that the path to knowledge isn't the exclusive purview of the scientific method - the very nature of the scientific method has been shown by Gödel to be inadequate to COMPLETELY describe the Universe from our point inside of it - as UMP says, the possibility exists that we'll need a number of different systems for describing the Universe - which is what I think Virus has been saying all along, that we cannot rely on science alone, and that other methods of thought, such as metaphysics and such, are needed and are good methods for thought and shouldn't be discounted. Am I right in summarizing it that way?

... Hmmm, I've had time to peruse what I've written here, and I can't help but wonder if it is *I* that has a different view of the sceintific method than what is "classically" taught ... perhaps I've conscientiously modified the scientific method a bit from what it was classically meant or thought to do given my own studies of the theorems of quantum mechanics, general relativity, and Gödel's incompleteness. I'm starting to think that this may be the case, but modesty prevents me from arriving at that conclusion. I'm sure that it's really just a very common downfall of human nature to abuse the scientific method to DISproove things, or to expound the viewpoint exemplified by the horrendous statement that "all that is not scientific fact is crap." The fact is that I work with scientists who tend to be along the cutting edge (I happen to work at Los Alamos National Laboratories, which you might have heard about in the past ) of physics and stuff - perhaps I do have the wrong idea about what the scientific method is, but I don't think so. Perhaps what I think it is is what it OUGHT to be - regardless, it is how I was taught and how I feel it is the only valid way to interpret the ideals behind the method. Whichever the case is, no means of thought should remain stagnant and unchanging, but rather should grow and change with time and knowledge, especially science and the scientific method itself. Indeed, it seems that such a thought method would indicate that this is needed for its own survival - since we continuously come up with new ideas, we need to be prepared to modify our way of thinking to accomodate the new ideas and how the ideas and their implications affect the way we think.

Okay, I think I've said enough for now. I just wanted to try to tone down my own ideas about thought processes and clearly state that I'm not trying to be arrogant here with my assumptions about the scientific method as the only means of thought, or that it's flawless; indeed, I think it's a logical flaw to assume that any idea expounded through even the proper use of the scientific method is absolute truth. Come to think of it, there IS no absolute truth. As I've said before, and I'll say again, the only thing truly impossible is impossibility itself. How's THAT for a tautology?

- JD

ps: Virus, that was very flattering, being quoted in the same paragraph as Werner Heisenberg! Thank you.

No, I don't think the Librarian Paradox is quite the same paradox as the one used in the Incompleteness Theorem.

As far as I am aware Gödel came up with a mathematical formulation for this statement:

This statement cannot be proved using the formalisms of Number Theory.

So a very important aspect of what Gödel did was to show that such a statement could in fact be expressed using the formalisms of Number Theory. Merely because it can be expressed, it cannot be proved - because it states that it cannot be proved; if it could be proved, it would refute itself, and that cannot happen with the strict logic of Number Theory. So it is a true statement, and judging from outside the system of Number Theory we can see clearly that it must be true, but from the inside of Number Theory it cannot be proved to be true without violating logic.

Self-reference creates logical paradoxes, and all sentient beings have the ability to contemplate and refer to themselves. That is why a science of sentience, or consciousness, promises to enrich and enlarge the scope of traditional science.

Any comments?

I have not had time to think about UMPs latest message. In regard to JD's before that however -

I was suggesting that a the idea that conciousness may be in all things is, I suspect, 'in principle' untestable. In other words can never be tested, thus never disproved or proved by observation, thus not a meaningful statement in scientific terms. Of course if a test is developed in the future then I will be shown wrong. I am aware that if a statement can be tested, however unimaginable that test might be at present, then that statement remains meaningful. But if it is for some reason by definition untestable then it is generally belived not to be a meaningful statement. Nothing to do with provability here, just testability. I was not getting confused about the scientific method, I was accepting its rationale.

I did not expand on why I think this idea is untestable because I don't really think it matters. It has no bearing, in the end, on whether it is true or not.

I also do not believe that theories are good or bad. It may not even matter whether they are true or not. What matters is their usefulness. In other words I agree with JD on the pragmatic approach.

Where I do part company with much science is in its unquestioning acceptance of its roots. Outside the higher end of science this acceptance is interpreted as meaning we are certain of those roots. This is unfortunate because it stunts the growth of more useful ideas.

Science is more dependent on faith than many scientists like to admit. Hell, we don't even know what mass and inertia are. Is anyone starting out to learn physics made aware of that? No, they get the dogma. I can see my son getting it at school - don't question anything, just learn the facts. I have no problem with science, rationalism , the 'method, whatever. But science does not present an honest face to the public - so most people have a blind faith in the dogma.

This is not dissimilar to Christian theology over the centuries, where intellectual thought within the church ran far ahead of popular beliefs. People were not educated to understand, or even question, the roots of those beliefs.

Much left unsaid but must go.

Ah ha. I gotcha now, thanks for your patience, Virus. I have to agree with your points here, and it's something I find very frustrating as well. I've been saying for years that true science isn't taught in schools, as can be seen by the very experience your son is experiencing (which I, too, experienced in some schools as I'm sure the majority of us did). Particularly what bothers me is the dogmatic teaching of physics and other sciences - that is simply NOT teaching science! It's teaching scientific knowledge to people, very few of whom it is expected will ever need to know the difference between learning scientific knowledge as opposed to leaning the philosophy of scientific thought. This is an insult to the human mind, and I quite agree with Virus that this misguided approach we've been using is presenting a dishonest face to the public. It's one of the reasons I mentioned in the "What Do You Think Are The Most Important Qualities of a Teacher?" forum that I thought it far more crucial to teach how to learn rather than teach knowledge itself.

The quest for knowledge should be based primarily on how to take information gained through our senses (be they of the accepted five variety or some other form of inexplicable or extraordinary means), apply a framework of rules like logic and mathematics, and predict other behavior with some amount of accuracy. Knowledge gained that way has been the core of all modern technology, whether people ever heard of the scientific method or not - people are always practicing this method of learning, whenever they catch a baseball, do a backflip off of a diving board, wash their hands, or just turn on the TV. Also, when I say senses, I'm not excluding anything outside of our "normal" five senses (see, smell, taste, touch, and hear). To discount anything just because it cannot be conclusively proven is foolish and contrary to science (indeed, since nothing can be proven anyway, the word seems to require a new meaning). Many of the greatest contributions towards science have been started by such logical leaps that can only be described as "inspired" ... which doesn't really explain how the person came up with the idea, how they performed the thoughts that no one else had ever done to come up with the explanation. Perhaps where I feel the scientific method could still be applied, or indeed IS still applied, is that it makes no specification about how observations are acquired nor on how they are manipulated in our brains to come up with something that can be tested. I wonder if perhaps our "common" and "taught" definition of science has corrupted us so far that we cannot go back to the roots of the philosophy of science and avoid further damage ... it seems very plain to me that this is not only going to require great effort on the part of our teachers, but especially on those that have already "learned" science the wrong way.

I have to point out this is (like everything else anyone says anywhere) my own view, and that I could easily have the wrong idea about what science has been taught. However, I find it distinctly disheartening and unnecessarily self-flattering to think that I alone think the true tenets of science have been violated and I'm crusading against a dogmatic brainwashing of our culture the likes of which has not been seen since the Middle Ages. I'm no prophet, and wouldn't want the job if you paid me. But on the other hand, if I'm right is assuming that other people do indeed agree that the "science" that is taught in schools is wrong, then why are we allowing it to continue? It all boils down to convenience, if you ask me, though I think that's making a mockery of the problem since it's probably more convenient to teach people HOW to learn rather than make them memorize information they have no interest in. Not only is it a problem of being efficient, it's a problem of how we as a society understand each other and appreciate each other's roles. After all, as one of my fellow engineers said in the movie 'Brazil' ... "We're all in it together, kid!"

- JD

Spot on JD and well put. I think the answer is that your average school teachers are not the sort of people to approach their subject, whatever it is, with the kind of approach you suggest. They have to get kids through exams and their performance is measured on this.

Also, having initially trained as a musician alongside many students who were training to be teachers, the simple fact is that in general teachers are not thinkers in a real sense. The two activities do not go together at anything much less than post graduate level.

Anyway, we have reached resting place of agreement which is good. (Someone ought to study the dynamics of email, as opposed to face to face, discussions, they are very different. It's so easy to write something you don't quite mean, have no immediate chance to explain what you did mean, and end up defending a point you never meant to make in the first place).

Bye for now.

But because it's so easy to be misunderstood, we must go to extra trouble with what we write, we have to think more clearly, take more pains, work harder at giving a detailed but not confusing explanation. I think it's a very good way to exercise the communication muscles!

We are now all in agreement: I too believe that we must teach people HOW to learn, and HOW to THINK! Have any of you two heard of Edward de Bono?